The outer oblique boundary problem of potential theory

  • In this article we prove existence and uniqueness results for solutions to the outer oblique boundary problem for the Poisson equation under very weak assumptions on boundary, coefficients and inhomogeneities. Main tools are the Kelvin transformation and the solution operator for the regular inner problem, provided in [1]. Moreover we prove regularisation results for the weak solutions of both, the inner and the outer problem. We investigate the non-admissible direction for the oblique vector field, state results with stochastic inhomogeneities and provide a Ritz-Galerkinm approximation. The results are applicable to problems from Geomathematics, see e.g. [2] and [3].

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Metadaten
Author:Thomas Raskop, Martin Grothaus
URN (permanent link):urn:nbn:de:hbz:386-kluedo-16098
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (43)
Document Type:Preprint
Language of publication:English
Year of Completion:2009
Year of Publication:2009
Publishing Institute:Technische Universität Kaiserslautern
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

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